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Pairs of additive congruences: cubic congruences

Published online by Cambridge University Press:  26 February 2010

R. J. Cook
R. J. Cook
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH
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Abstract

We consider two additive cubic equations

in p-adic fields. Davenport and Lewis showed that the equations have a non-trivial solution in every p-adic field, if n ≥ 16, and need not have a solution in the 7-adic field, if n = 15. Here we prove that if p ≠ 7 the equations have a non-trivial solution in p-adic fields if n ≥ 13. When n = 12 such a result fails for every prime p ≡ 1 (mod 3).

Type
Research Article
Information
Mathematika , Volume 32 , Issue 2 , December 1985 , pp. 286 - 300
Copyright
Copyright © University College London 1985

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